In a set of proposals published on its website, Deutsche Boerse also suggested index bans for companies that fail to submit quarterly figures on time.
"It is no secret that I personally would welcome the expansion of the DAX 30 to a DAX 40," Deutsche Boerse Chief Executive Theodor Weimer said in an emailed statement.
Since its founding in 1988, the DAX has been Germany's answer to the Dow Jones Industrial Average in New York and the FTSE in London, with 30 members forming the corporate elite in one of the world's largest economies.
Most of the index's founding members have since dropped out.
The most recent departure was payments company Wirecard, which in a blow to Germany's capital markets, filed for insolvency just two years after its promotion to the index. The payments company owed creditors billions in what auditor EY described as a sophisticated global fraud.
Weimer has since changed rules to allow for a quicker expulsion of companies in the wake of the scandal.
The rules proposed on Monday would make proven profitability a requirement for joining the DAX.
The proposal also suggested reducing the number of constituents in the mid-cap index to 50 from 60.
Companies where sales of controversial weapons make up more than 10% of revenue should also be excluded from the DAX selection indices, which include the DAX, MDAX, TecDAX and SDAX, Deutsche Boerse said.
Investors now have until Nov. 4 to respond to the proposal. Deutsche Boerse said it would publish the results of the consultation and any decision on changes to the index rules, by Nov. 23.
(Reporting by Hans Seidenstuecker; writing by Caroline Copley and Tom Sims; Editing by Riham Alkousaa, Maria Sheahan and Tomasz Janowski)